Here's a tidyverse solution. I've reproduced just the first 4 rows and columns of your data to illustrate.
library(dplyr, warn.conflicts = FALSE)
#> Warning: package 'dplyr' was built under R version 3.6.3
data <- tribble(~ S1_261059, ~ S1_330484, ~ S1_623981, ~ S1_656912,
"C", "G", "A", "T",
"C", "G", "A", "C",
"C", "G", "G", "T",
"T", "G", "A", "C")
data %>% mutate_all(~ case_when(. == "A" ~ 1,
. == "T" ~ 2,
. == "C" ~ 3,
. == "G" ~ 4))
#> # A tibble: 4 x 4
#> S1_261059 S1_330484 S1_623981 S1_656912
#> <dbl> <dbl> <dbl> <dbl>
#> 1 3 4 1 2
#> 2 3 4 1 3
#> 3 3 4 4 2
#> 4 2 4 1 3
Created on 2020-04-09 by the reprex package (v0.3.0)
By the way, do those "A", "C", "G" and "T" represent the 4 DNA bases?